Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
From inside the book
Results 1-5 of 48
Page 21
... intersect each other , they form four angles about the point of intersection , which have received different names , with respect to each other . 1 ° . ADJACENT ANGLES are those which lie on the same side of one line , and on opposite ...
... intersect each other , they form four angles about the point of intersection , which have received different names , with respect to each other . 1 ° . ADJACENT ANGLES are those which lie on the same side of one line , and on opposite ...
Page 23
... intersect in only one point . NOTE . The method of demonstration employed above , is called the reductio ad absurdum . It , consists in assuming an hypothesis which is the contradictory of the proposition to be proved , and then ...
... intersect in only one point . NOTE . The method of demonstration employed above , is called the reductio ad absurdum . It , consists in assuming an hypothesis which is the contradictory of the proposition to be proved , and then ...
Page 26
... intersection D ( P. III . , C. ) : hence , the triangles coincide throughout , and are therefore equal in all respects ( I. , D. 15 ) ; which was to be proved . PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is ...
... intersection D ( P. III . , C. ) : hence , the triangles coincide throughout , and are therefore equal in all respects ( I. , D. 15 ) ; which was to be proved . PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is ...
Page 37
... intersect two other straight lines AB and CD , it is called a secant , with respect to them . The eight angles formed about the points of intersection have different different names , with respect to each other . 1 ° . INTERIOR ANGLES ...
... intersect two other straight lines AB and CD , it is called a secant , with respect to them . The eight angles formed about the points of intersection have different different names , with respect to each other . 1 ° . INTERIOR ANGLES ...
Page 41
... intersect a third straight line , making the sum of the interior angles on interior angles on the same side less than two right angles , the two lines will meet if suffi- ciently produced . Let the two lines CD , IL , meet the line EF ...
... intersect a third straight line , making the sum of the interior angles on interior angles on the same side less than two right angles , the two lines will meet if suffi- ciently produced . Let the two lines CD , IL , meet the line EF ...
Other editions - View all
Common terms and phrases
ABCD AC² adjacent angles altitude apothem Applying logarithms bisects centre chord circle circumference circumscribed cone consequently convex surface cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle inscribed intersection isosceles less Let ABC log sin lower base lune mantissa number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron principle demonstrated prism PROBLEM.-In PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment semi-circumference similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square straight line subtracting supplement Tang tangent THEOREM THEOREM.-Show tri-rectangular triangle ABC triangular prism triedral angle upper base vertex vertices volume whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 90 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 18 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 253 - For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...
Page 61 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 94 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Page 126 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 125 - THEOREM. Similar triangles are to each other as the squares of their homologous sides.